The essential difference between these two types of purchases is their payment status on entry.
Bills are invoices issued towards your business which need to be paid. Adding them in the application gives you the option of getting a notification for when your bill needs to be paid, thus assisting you with keeping track of your financial obligations. It will keep appearing as unpaid unless a payment is entered.
An expense entry, on the other hand, can be used for business expenses already been paid: purchases, payroll, rent can all be added there. There is no need for additional clicks to indicate that payment has been fulfilled.
When it comes to adding expenses, entering a supplier is optional so is the distribution of the expenses in product lines. This also, means, however, that it is not directly connected to the inventory. To make sure stock management is automated, opt for adding a bill instead.
Regardless of the form you choose to proceed with, you will still be able to select expense categories and get full reporting on expenses, payments and bills.
Last but not least, you may also associate expenses and bills with projects you have been working on and if you wish, bill them to your clients.